This article presents vibration and dynamic stability analysis of Functionally Graded Ordinary (FGO) beam and Functionally Graded Sandwich (FGSW) beam with simply supported ends and resting on Pasternak elastic foundation. The material properties distribution along the thickness of the beams is assumed to follow either exponential law or power law. Finite element method in conjunction with Hamilton’s principle is used to establish the governing equation of motion. Floquet’s theory is used to establish the stability boundaries. The first two mode frequencies of FGO and FGSW beam increase with the increase in stiffness of the foundation. It is also observed that exponential distribution of properties ensures better dynamic stability of both FGO and FGSW beams compared to power law distribution of properties. The foundation enhances the dynamic stability of both the beams.